This will generally work okay provided that the water heater give enough BTU.
Because the radiant heating water and domestic hot water are commingled, it is possible to turn on the faucet and get only lukewarm water if the space heating part of the system just kicked on and the floors were quite cool, pulling down the temperature of the entire "body of water".
Is this considered a "normal" installation? Given all the pipework as shown, how hard would it be to extricate the water heater and replace when it springs a leak? Also the warranty may be voided by this usage.
Tornado victims: Do not rush to rebuild. Take your time and look for and get a good contractor. Or consider selling the property and moving to a home that is ready to live in.